Chemnitz – IWIS2012 – Tutorial 6, September 26, 2012

1. Chemnitz – IWIS2012 – Tutorial 6, September 26, 2012 Electronics and Signals in Impedance Measurements byMart Min min@elin.ttu.ee Thomas Johann Seebeck Department of Electronics, Tallinn University of TechnologyTallinn, Estonia

2. Old Hansestadt Reval – Today’s Tallinn • Tallinn/ Reval was: • - a member of the Hanseatic League (since 1285) • - ruled under the Lübeck City Law (1248-1865) • - capital of the Soviet Socialist Republic of Estonia within the Soviet Union (1940-1991) • Tallinn is: • capital of the Republic of Estonia, EU member state since 2004 • currency: EURO since Jan 2011

3. What is impedance ? ______________________________________________________________________________ Ohm's law, published in 1826: The term was introduced by OliverHeaviside,mathematician, physicist, and self-taught engineer: July 1886 -impedance Dec 1887 –admittance In 1893, Arthur Edwin Kennelly presented apaper “on impedance" to theAmerican Institute of Electrical Engineers in which he discussed the first use of complex numbers as applied to Ohm's Law forAC Electrical impedance(or simply impedance) is a measure of opposition to sinusoidal electric current The concept of electrical impedance generalizes Ohm's law to AC circuit analysis. Unlike electrical resistance, the impedance of an electric circuit can be a complex number:Z = V/I, where Z = R + jX, and R is a real part and X is an imaginary part.

4. Dynamic system identification is the final aim!

5. Goal: making the identification faster and simpler!

6. Both magnitude (amplitude) and phase are to be measured Im Ż Ż = R + j X Re Ż Re Ż = R F Magnitude and phase measurement ç Ż Im Ż = X Ż = R + j X ç

7. Synchronous or phase-sensitive detection Synchronous detection phase lag Φ phasephase lag Φ lag Φ Synchronous or phase sensitive detection (demodulation) suppresses additive noise and disturbances and gives the results (Re or Im) in Cartesian coordinates

8. Two-phase or quadrature synchronous detection Fourier Transform Two-phase (inphase and quadrature, I&Q) synchronous detection (the simpliest Fourier Transform) enables simultaneous measurement of Re and Im parts

9. Problems to be solved Impedance should be measured at several frequencies – a wide band spectral analysis is required. Impedance is dynamic - the spectra are time dependent. Examples: (a) cardiovascular system; (b) pulmonary system; (b) microfluidic device. Classical excitation – a sine wave – enables slow measurements. Excitation must be: 1) as short as possible to avoid significant changes during the spectrum analysis; 2) as long as possible to enlarge the excitation energy for achieving max signal-to-noise ratio. Which waveform is the best one? A unique property of chirp waveforms – scalability – enables to match the above expressed contradictory requirements (1) and (2) and the needs for spectrum bandwidth (BW), excitation time (Texc), and signal-to-noise ratio (S/N). The questions to be answered: a.A chirp wave excitation contains typically hundreds and thousands of cycles, if the impedance changes slowly. What could be the lowest number of cycles applicable when fast changes take place? b. Are there any simpler rectangular waveforms to replace the sine waves and chirps in practical spectroscopy?

10. Focus:finding the best excitation waveforms for the fast and wideband time dependent spectral analysis: intensity (Re & ImorM & φ) versus frequency ωand time t

11. Signals and signal processing in wideband impedance spectroscopy Focus:finding the best excitation waveforms and signal processing methodsfor the fast and wideband, scalable, and time dependent spectral analysis: intensity (Re & ImorM & Φ) versus frequency ωand time t excitation, Vexc response, Vz Ż Fourier Transform (DFT, FFT) Generation of excitation waveform Cross correlation C{Vz(t),Vr(t,τ)} Impedance spectrogram gz(t) time: t1 to t2 Excitation control Sz (jω,t) freq: f1 to f2 reference, Vr A A A a – short rectangular pulse t1 t2 t2 t1 t1 - very high CF (10 to 1000) - BW = 0 to 0.44(1/Δt), - low signal energy, -not scalable Δt c – binary sequence (chirp pulse) from t1 to t2 covers BW from f1 to f2 , scalable, ideal CF=1.0 b – chirp pulse (t1 to t2) covers BW (f1 to f2), scalable, acceptable CF=1.414 Crest factor CF = Peak / RMS

12. Several sine waves simultaneously – Multisine excitation Fast simultaneous measurement at the specific frequencies of interest! +Simultaneous measurement/analysis; + Frequencies can be chosenfreely; +/- Signal-to-noise level is low but acceptable; − Both limited excitation energy and complicated signal processing restrict the number of different frequency components.

13. Sine wave signals and synchronous sampling: multisite and multifrequency measurement Multisite(frequency distinction method, slightly different f1 and f2) Multifrequency (sum of very different frequency sine waves)

14. Multisine excitation: optimization (a sum of 4 equal level sine wave components – 1, 3, 5, 7f) Sum of 4 sine waves Ai =1, Φi =opt, CF=1.45 (the best possible case) Sum of 4 sine waves Ai =1, Φi = 0, CF=2.08 Sum of 4 sine waves Ai =1, Φi =900, CF=2.83 (theworst possible case) RMS levels of sine wave components in the multisine signal Sine waves: A=1, RMS = 0.707 the best case Φi = opt; 0.344 Φi = 0;0.241 Φi = 90;0.177 the worst case Normalized to ∑Ai = 1, Φi = opt:Vrmsi = 0.344, CF=1.45 Normalized to ∑Ai = 1, Φi = 0:Vrmsi = 0.241, CF= 2.08

15. Waveforms of wideband excitation signalsCrest Factor CF = (max level) / RMS value ∫ ≈ ≈ ≈ ≤ ≈ ≥

16. Scalable chirp signals: two chirplets 1 t 2.24 mV/Hz1/2 1mV / Hz1/2 1.12 mV/Hz1/2 BW= 100 kHz BW = 400 kHz Texc = 250 μs A.Scalability in frequency domain: bandwidth BWchanges, Texc = const = 250 μs 48cycles 12cycles Texc = 1000 μs Excitation time Texc= 250 μs= const Excitation energyEexc= 0.5V2 ∙250μs=125V2∙μs Voltage Spectral Density @ 100kHz=2.24mV/Hz1/2 Voltage Spectral Density @ 400kHz=1.12mV/Hz1/2 Changes in the frequency span BW reflect in spectral density

17. Scalable chirp signals: two chirplets 2 Texc = 250 μs Texc = 1000 μs 4.48mV/Hz1/2 2.24mV/Hz1/2 1mV / Hz1/2 BW = 100 kHz B. Scalability in time domain: duration Texc changes, BW= const = 100 kHz 12cycles 48cycles Bandwidth BW=100 kHz= const Energy E250μs= 125V2∙μs Energy E1000μs= 500V2∙μs Voltage Spectral Density @250μs=2.24mV/Hz1/2 Voltage Spectral Density @ 1000μs=4.48mV/Hz1/2 Changes in the pulse duration Texc reflect in spectral density

18. A very short Chirplet 3 - Half-cycle linear titlet RMS spectral density (relative) 10 1 10-1 10-2 10-3 10-4 -40 dB/dec 2.26 mV/Hz1/2 1k 10k 100k 1M f, Hz Tch =10μs 100kHz Texc = Tch =10μs, BW = 100 kHz Instant frequency, , rad/s - a linear frequency growth Current phase , rad; Generated chirplet

19. The current switch operates as a multiplier! I I + + Vout I-to-V V-to-I – I – Vin A1 = (4/π)A > A t S1 S2 A1 Driving transor Clock Flip-Flop 13579 11 13 15 17 19 21 23 25h t h = 1, 3, 5, 7, 9, 11, A1 9111315171 Rectangular (binary) wave based impedance measurement A problem: sensitivity to all the odd higher harmonics ! contains the products of all odd higher harmonics in addition to the response to signal component A1 A t A3 = (4/3π)A A5 = (4/5π)A h = 1, 3, 5, 7, 9, 11, ...

20. Ternary signals – waveforms and spectra FIG. 2B excitation -111 reference 1st - coinciding spectral lines 7th 11th 3rd 13th 17th 5th 19th 23rd 25th 9th

21. Ternary signal processing – 3-positional synchronous switching

22. Generator of binary and ternary signals Ternary 3-level signals Binary 2-level signals

23. (a) (b) (c) Different rectangular waveforms (binary and ternary) of excitation signals (a) – binary (2-state) chirp, scalable; (b) – binary pseudorandom (MLS), not scalable, waveform is quitesimilar to the multifrequency binary signal, see next slide (c) – ternary (3-state) chirp, scalable.

24. 0 18 30 Spectra and power of binary/ternary chirps Binary(0) Trinary(30) 100kHz Pexc– excitation power within (BW)exc=100kHz Ternary(18): Pexc0.93P Binary(0): Pexc= 0.85P Ternary(30): Pexc0.92P Trinary (21.2): Pexc=0.94P – max. possible!

25. Synthesized multifrequency binary sequences (4 components – 1, 3, 5, 7f) A simple rectangular waveform Decreasing levels: usual case! Equal-level components Growing-level components !

26. Example: optimized multifrequency binary sequence (14 binary rated components – 1, 2, 4, 8f,...,8192f) A section of one binary wave sequence: 14 frequency components and 81920 samples The spectrum contains 14 components at 1, 2, 4, 8f,..., until 8192f with mean RMS value of 0.22 each. Max level deviation is +/- 3.5 %; 67% of the total energy is concentrated onto desired frequencies While multisinesignals concentrate all the energy into wanted spectral lines, the binaryones only about 60 to 85% Despite of losses (15 to 40%), the energy of the desired frequency components in binary sequences have greater value than the comparable components in multisine signals ! 26

27. How to make a current sources Cparasitic is a problem Cparasitic Based on diamond transistor Based on current feedback

28. How to make passive current sources is a problem Cparasitic Simple resistive V-to-I converter Compensated resistive V-to-I converter

29. Howland current source is a problem Cparasitic Tends to be unstable (both negative and positive feed-backs)

30. How to make the current excitation better and to couple the excitation signal with the impedance to be measured Cparasitic We designed a current source using differential difference amplifier. We got the output impedance: 250 kΩ. At higher frequencies a part of excitation currentis flowingdown through a parasitic capacitance 40pF. We added a voltage follower (more exactly, an amplifier with a gain 0.9) and reduced the parasitic capacitance about 10 times !

31. How to make the excitation more accurate? Cparasitic We added a trans-impedance amplifier for the measurement of excitation current. Result – degradation of the current source at higher frequencies can be taken into account An alternative: voltage measurement on a shunt

32. How to measure voltage drop across the impedance Instrumentation amplifier (IA) Solution Good BW can be reached when the IA is constructed from separate high performance op-amps. Magnitude Phase Voltage aquisition amplifier

33. 1) Frequency stepping or sweeping together with multiplexing of traditional sine wave excitation is too time consuming, especially when the dynamic impedances are to be measured.2) Simultaneous applying of several sine wave excitations with different frequencies (multisine) is a better, but more complicatedsolution. 3) We propose specific chirp based excitation signals as chirplets and titlets, also binary and ternary chirps and chirpletsfor carrying out the fast and wide band scalable spectroscopy of dynamic objects.4) Also multi-sine binary and ternary (trinary) signalsare proposed for excitationsin impedance spectroscopy and tomography.5) Synthesis of the above mentioned excitation signals enables to provide independent,time and frequency domain scalable spectroscopy, which is adaptable to given measurement situation (speed of impedance variations, frequency range, S/N level).6) Use discrete and digital signal generation/processing methods as much as possible, but you can never avoid analog part of the measuring system.7) Be careful with current sources, avoid if possible.8) Using of field programmable gate arrays (FPGA) is challencing. Both, microcontrollers and signal processors, make troubles with synchronising and throughput speed. Summary